List questions from noncommutative-algebra

Published on 17 Nov 2017 - 18:18

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Show that subtraction of matrices is neither commutative nor associative. Please review my work.

Published on 26 Mar 2026 - 12:49

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Isomorphism between two generalized quaternions algebras

Published on 20 Nov 2017 - 21:11

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Rings such that there are finitely many modules of a given length

Published on 23 Nov 2017 - 10:05

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A ring without multiplicative identity in which the only ideals are (0) and the whole ring

Published on 27 Nov 2017 - 6:28

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An example of a non-commutative ring with multiplicative identity 1 in which the only (two sided) ideals are 0 and the whole ring

Published on 28 Nov 2017 - 6:19

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Can the commutator $[A,\,B]$ be derived if $\left[A,\,B^2\right]$ is known?

Published on 28 Nov 2017 - 22:44

169

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Diagonalizing a matrix of operators

Published on 26 Mar 2026 - 7:57

235

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Multiplicities in the Regular Representation of a Semisimple Algebra

Published on 07 Dec 2017 - 17:53

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A problem of central simple algebras: why $(E,s,\gamma)\cong M_n(F)$ only if $\gamma$ is the norm of an element of $E$?

Published on 23 Feb 2026 - 11:23

74

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$R$ is simple iff $M_n(R)$ is simple for rings without identity

Published on 08 Dec 2017 - 19:37

175

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Show that $(X+Y+Z)^n = X^n + Y^n + Z^n$ if $XY = qYX$ and $YZ = q ZY$ and $ZX = qX Z$

Published on 27 Mar 2026 - 1:48

22

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$\frac{\text{Radical}(M)}{K}\subseteq \text{Radical}(M/K)$

Published on 19 Dec 2017 - 11:59

30

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Non-commutative Babylonian-ish multiplication formula?

Published on 19 Dec 2017 - 12:21

228

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Socle of a quotient ring

Published on 23 Feb 2026 - 7:41

List Question

Finite order of an element in Brauer group.

Show that subtraction of matrices is neither commutative nor associative. Please review my work.

Isomorphism between two generalized quaternions algebras

Rings such that there are finitely many modules of a given length

A ring without multiplicative identity in which the only ideals are (0) and the whole ring

An example of a non-commutative ring with multiplicative identity 1 in which the only (two sided) ideals are 0 and the whole ring

Can the commutator $[A,\,B]$ be derived if $\left[A,\,B^2\right]$ is known?

Diagonalizing a matrix of operators

Multiplicities in the Regular Representation of a Semisimple Algebra

A problem of central simple algebras: why $(E,s,\gamma)\cong M_n(F)$ only if $\gamma$ is the norm of an element of $E$?

$R$ is simple iff $M_n(R)$ is simple for rings without identity

Show that $(X+Y+Z)^n = X^n + Y^n + Z^n$ if $XY = qYX$ and $YZ = q ZY$ and $ZX = qX Z$

$\frac{\text{Radical}(M)}{K}\subseteq \text{Radical}(M/K)$

Non-commutative Babylonian-ish multiplication formula?

Socle of a quotient ring

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